A Novel Hybrid Algorithm for the Forward Kinematics Problem of 6 DOF Based on Neural Networks.

The closed kinematic structure of Gough-Stewart platforms causes the kinematic control problem, particularly forward kinematics. In the traditional hybrid algorithm (backpropagation neural network and Newton-Raphson), it is difficult for the neural network part to train different datasets, causing training errors. Moreover, the Newton-Raphson method is unable to operate on a singular Jacobian matrix. In this study, in order to solve the forward kinematics problem of Gough-Stewart platforms, a new hybrid algorithm is proposed based on the combination of an artificial bee colony (ABC)-optimized BP neural network (ABC-BPNN) and a numerical algorithm. ABC greatly improves the prediction ability of neural networks and can provide a superb initial value to numerical algorithms. In the design of numerical algorithms, a modification of Newton's method (QMn-M) is introduced to solve the problem that the traditional algorithm model cannot be solved when it is trapped in singular matrix. Results show that the maximal improvement in ABC-BPNN error optimization was 46.3%, while the RMSE index decreased by 42.1%. Experiments showed the feasibility of QMn-M in solving singular matrix data, while the percentage improvement in performance for the average number of iterations and required time was 14.4% and 13.9%, respectively.